B) If a Hudson lane makes 57° angle with M.G. road and H.M. road making 37°, with M.G. road, then which type of angle does form between Hudson lane and H.M. road?
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Answers & Comments
Step-by-step explanation:
The measure of acute angle between Akbar Road and Hudson Lane can be found by subtracting the given angle from 90 degrees (since Akbar Road and M.G Road form a right angle):
90° 57° 33°
Therefore, the acute angle between Akbar Road and Hudson Lane is 33 degrees.
ii) The reflex angle formed between M.G Road and Hudson Lane can be found by adding the given angle with 180 degrees (since reflex angle is greater than 180 degrees): 180° 57° = 237°
Therefore, the measure of reflex angle formed between M.G Road (in east direction) with Hudson Lane is 237 degrees.
iii) To find the shortest angle they can cover in order to meet, we need to find the acute angle between H.M. Road and M.G. Road at their intersection point. Let's call this angle x.
Since Akbar Road and M.G. Road form a right angle,we know that the angle between H.M. Road and Akbar
Road is also x. Thus, the angle between H.M. Road and
Akbar Road is:
90° - x
Since the sum of angles around the intersection point
must be 360 degrees, we can write:
x + (90° - x) + 180° + (180° - x) = 360°
Simplifying this equation gives:
450°-3x 360°
Subtracting 360° from both sides gives:
90° - 3x = 0
Adding 3x to both sides gives:
90° = 3xDividing both sides by 3 gives:
x = 30°
Therefore, the shortest angle they can cover in order to meet is 30 degrees.